Skip to main content
Chemistry LibreTexts

Untitled Page 5

  • Page ID
    180900
  • Chapter 1

    Values, Types, and Operators

    Untitled Page 5#p_93S4YBaGUfBelow the surface of the machine, the program moves. Without effort, it expands and contracts. In great harmony, electrons scatter and regroup. The forms on the monitor are but ripples on the water. The essence stays invisibly below.

    Master Yuan-Ma, The Book of Programming
    chapter_picture_1.jpg

    Untitled Page 5#p_sgNSYKwqboInside the computer’s world, there is only data. You can read data, modify data, create new data—but that which isn’t data cannot be mentioned. All this data is stored as long sequences of bits and is thus fundamentally alike.

    Untitled Page 5#p_W1gJpe5a7/Bits are any kind of two-valued things, usually described as zeros and ones. Inside the computer, they take forms such as a high or low electrical charge, a strong or weak signal, or a shiny or dull spot on the surface of a CD. Any piece of discrete information can be reduced to a sequence of zeros and ones and thus represented in bits.

    Untitled Page 5#p_PDoqiRoGSaFor example, we can express the number 13 in bits. It works the same way as a decimal number, but instead of 10 different digits, you have only 2, and the weight of each increases by a factor of 2 from right to left. Here are the bits that make up the number 13, with the weights of the digits shown below them:

       0   0   0   0   1   1   0   1
     128  64  32  16   8   4   2   1

    Untitled Page 5#p_0u8qQ2tfMISo that’s the binary number 00001101. Its non-zero digits stand for 8, 4, and 1, and add up to 13.

    Untitled Page 5#h_sVZPaxUSy/Values

    Untitled Page 5#p_ySnc2wG5kfImagine a sea of bits—an ocean of them. A typical modern computer has more than 30 billion bits in its volatile data storage (working memory). Nonvolatile storage (the hard disk or equivalent) tends to have yet a few orders of magnitude more.

    Untitled Page 5#p_JRdY+sw4TVTo be able to work with such quantities of bits without getting lost, we must separate them into chunks that represent pieces of information. In a JavaScript environment, those chunks are called values. Though all values are made of bits, they play different roles. Every value has a type that determines its role. Some values are numbers, some values are pieces of text, some values are functions, and so on.

    Untitled Page 5#p_+ayfFmFdzeTo create a value, you must merely invoke its name. This is convenient. You don’t have to gather building material for your values or pay for them. You just call for one, and whoosh, you have it. They are not really created from thin air, of course. Every value has to be stored somewhere, and if you want to use a gigantic amount of them at the same time, you might run out of memory. Fortunately, this is a problem only if you need them all simultaneously. As soon as you no longer use a value, it will dissipate, leaving behind its bits to be recycled as building material for the next generation of values.

    Untitled Page 5#p_lWUuVOz1PdThis chapter introduces the atomic elements of JavaScript programs, that is, the simple value types and the operators that can act on such values.

    Untitled Page 5#h_flOCH3CuFgNumbers

    Untitled Page 5#p_lB/BspzEbzValues of the number type are, unsurprisingly, numeric values. In a JavaScript program, they are written as follows:

    13

    Untitled Page 5#p_nFVjE3kHJhUse that in a program, and it will cause the bit pattern for the number 13 to come into existence inside the computer’s memory.

    Untitled Page 5#p_TBpgYLjzVrJavaScript uses a fixed number of bits, 64 of them, to store a single number value. There are only so many patterns you can make with 64 bits, which means that the number of different numbers that can be represented is limited. With N decimal digits, you can represent 10N numbers. Similarly, given 64 binary digits, you can represent 264 different numbers, which is about 18 quintillion (an 18 with 18 zeros after it). That’s a lot.

    Untitled Page 5#p_WcfWpTcQB6Computer memory used to be much smaller, and people tended to use groups of 8 or 16 bits to represent their numbers. It was easy to accidentally overflow such small numbers—to end up with a number that did not fit into the given number of bits. Today, even computers that fit in your pocket have plenty of memory, so you are free to use 64-bit chunks, and you need to worry about overflow only when dealing with truly astronomical numbers.

    Untitled Page 5#p_qgS+bpqvEkNot all whole numbers less than 18 quintillion fit in a JavaScript number, though. Those bits also store negative numbers, so one bit indicates the sign of the number. A bigger issue is that nonwhole numbers must also be represented. To do this, some of the bits are used to store the position of the decimal point. The actual maximum whole number that can be stored is more in the range of 9 quadrillion (15 zeros)—which is still pleasantly huge.

    Untitled Page 5#p_+wzyK91zcbFractional numbers are written by using a dot.

    9.81

    Untitled Page 5#p_oofHxZNW9MFor very big or very small numbers, you may also use scientific notation by adding an e (for exponent), followed by the exponent of the number.

    2.998e8

    Untitled Page 5#p_YbACmHw8KdThat is 2.998 × 108 = 299,800,000.

    Untitled Page 5#p_8KgYC0F1fXCalculations with whole numbers (also called integers) smaller than the aforementioned 9 quadrillion are guaranteed to always be precise. Unfortunately, calculations with fractional numbers are generally not. Just as π (pi) cannot be precisely expressed by a finite number of decimal digits, many numbers lose some precision when only 64 bits are available to store them. This is a shame, but it causes practical problems only in specific situations. The important thing is to be aware of it and treat fractional digital numbers as approximations, not as precise values.

    Untitled Page 5#i_RfBT3HMnYsArithmetic

    Untitled Page 5#p_PO8MaZIpG1The main thing to do with numbers is arithmetic. Arithmetic operations such as addition or multiplication take two number values and produce a new number from them. Here is what they look like in JavaScript:

    100 + 4 * 11

    Untitled Page 5#p_Gbkt+ofKYQThe + and * symbols are called operators. The first stands for addition, and the second stands for multiplication. Putting an operator between two values will apply it to those values and produce a new value.

    Untitled Page 5#p_UaADJxNSjABut does the example mean “add 4 and 100, and multiply the result by 11,” or is the multiplication done before the adding? As you might have guessed, the multiplication happens first. But as in mathematics, you can change this by wrapping the addition in parentheses.

    (100 + 4) * 11

    Untitled Page 5#p_OSF05nVTV6For subtraction, there is the - operator, and division can be done with the / operator.

    Untitled Page 5#p_sJXEzZnGO0When operators appear together without parentheses, the order in which they are applied is determined by the precedence of the operators. The example shows that multiplication comes before addition. The / operator has the same precedence as *. Likewise for + and -. When multiple operators with the same precedence appear next to each other, as in 1 - 2 + 1, they are applied left to right: (1 - 2) + 1.

    Untitled Page 5#p_epF5qxonWYThese rules of precedence are not something you should worry about. When in doubt, just add parentheses.

    Untitled Page 5#p_3aZxtaabKDThere is one more arithmetic operator, which you might not immediately recognize. The % symbol is used to represent the remainder operation. X % Y is the remainder of dividing X by Y. For example, 314 % 100 produces 14, and 144 % 12 gives 0. The remainder operator’s precedence is the same as that of multiplication and division. You’ll also often see this operator referred to as modulo.

    Untitled Page 5#i_R4eFf8w7YzSpecial numbers

    Untitled Page 5#p_JBBwZano0eThere are three special values in JavaScript that are considered numbers but don’t behave like normal numbers.

    Untitled Page 5#p_Vk/nIi3mWMThe first two are Infinity and -Infinity, which represent the positive and negative infinities. Infinity - 1 is still Infinity, and so on. Don’t put too much trust in infinity-based computation, though. It isn’t mathematically sound, and it will quickly lead to the next special number: NaN.

    Untitled Page 5#p_kS+V22+tDpNaN stands for “not a number”, even though it is a value of the number type. You’ll get this result when you, for example, try to calculate 0 / 0 (zero divided by zero), Infinity - Infinity, or any number of other numeric operations that don’t yield a meaningful result.

    Untitled Page 5#h_OBbEvqxHHHStrings

    Untitled Page 5#p_JUYnmsnZEAThe next basic data type is the string. Strings are used to represent text. They are written by enclosing their content in quotes.

    `Down on the sea`
    "Lie on the ocean"
    'Float on the ocean'

    Untitled Page 5#p_J5Re/uQFh3You can use single quotes, double quotes, or backticks to mark strings, as long as the quotes at the start and the end of the string match.

    Untitled Page 5#p_zqSxAQbLwwAlmost anything can be put between quotes, and JavaScript will make a string value out of it. But a few characters are more difficult. You can imagine how putting quotes between quotes might be hard. Newlines (the characters you get when you press enter) can be included without escaping only when the string is quoted with backticks (`).

    Untitled Page 5#p_Fhyuks46v3To make it possible to include such characters in a string, the following notation is used: whenever a backslash (\) is found inside quoted text, it indicates that the character after it has a special meaning. This is called escaping the character. A quote that is preceded by a backslash will not end the string but be part of it. When an n character occurs after a backslash, it is interpreted as a newline. Similarly, a t after a backslash means a tab character. Take the following string:

    "This is the first line\nAnd this is the second"

    Untitled Page 5#p_rtFNX67M4oThe actual text contained is this:

    This is the first line
    And this is the second

    Untitled Page 5#p_RcQxEVsohZThere are, of course, situations where you want a backslash in a string to be just a backslash, not a special code. If two backslashes follow each other, they will collapse together, and only one will be left in the resulting string value. This is how the string “A newline character is written like "\n".” can be expressed:

    "A newline character is written like \"\\n\"."

    Untitled Page 5#p_FkxXOQHt6aStrings, too, have to be modeled as a series of bits to be able to exist inside the computer. The way JavaScript does this is based on the Unicode standard. This standard assigns a number to virtually every character you would ever need, including characters from Greek, Arabic, Japanese, Armenian, and so on. If we have a number for every character, a string can be described by a sequence of numbers.

    Untitled Page 5#p_FZTkxxFJHyAnd that’s what JavaScript does. But there’s a complication: JavaScript’s representation uses 16 bits per string element, which can describe up to 216 different characters. But Unicode defines more characters than that—about twice as many, at this point. So some characters, such as many emoji, take up two “character positions” in JavaScript strings. We’ll come back to this in Chapter 5.

    Untitled Page 5#p_+y5+JTiKgRStrings cannot be divided, multiplied, or subtracted, but the + operator can be used on them. It does not add, but it concatenates—it glues two strings together. The following line will produce the string "concatenate":

    "con" + "cat" + "e" + "nate"

    Untitled Page 5#p_f802i8aCZiString values have a number of associated functions (methods) that can be used to perform other operations on them. I’ll say more about these in Chapter 4.

    Untitled Page 5#p_3NJXrCLWRRStrings written with single or double quotes behave very much the same—the only difference is in which type of quote you need to escape inside of them. Backtick-quoted strings, usually called template literals, can do a few more tricks. Apart from being able to span lines, they can also embed other values.

    `half of 100 is ${100 / 2}`

    Untitled Page 5#p_ogkFBzzZhiWhen you write something inside ${} in a template literal, its result will be computed, converted to a string, and included at that position. The example produces “half of 100 is 50”.

    Untitled Page 5#h_ygn12/ieo+Unary operators

    Untitled Page 5#p_GyQlmgK5IKNot all operators are symbols. Some are written as words. One example is the typeof operator, which produces a string value naming the type of the value you give it.

    console.log(typeof 4.5)
    // → number
    console.log(typeof "x")
    // → string

    Untitled Page 5#p_edv0ySDJvjWe will use console.log in example code to indicate that we want to see the result of evaluating something. More about that in the next chapter.

    Untitled Page 5#p_fvxC7oK7dTThe other operators shown all operated on two values, but typeof takes only one. Operators that use two values are called binary operators, while those that take one are called unary operators. The minus operator can be used both as a binary operator and as a unary operator.

    console.log(- (10 - 2))
    // → -8

    Untitled Page 5#h_cTPxJxlmFRBoolean values

    Untitled Page 5#p_OL3ZufvGREIt is often useful to have a value that distinguishes between only two possibilities, like “yes” and “no” or “on” and “off”. For this purpose, JavaScript has a Boolean type, which has just two values, true and false, which are written as those words.

    Untitled Page 5#i_Lfz4mKO9TgComparison

    Untitled Page 5#p_T4yLn4fXDHHere is one way to produce Boolean values:

    console.log(3 > 2)
    // → true
    console.log(3 < 2)
    // → false

    Untitled Page 5#p_j0tOwzfb6MThe > and < signs are the traditional symbols for “is greater than” and “is less than”, respectively. They are binary operators. Applying them results in a Boolean value that indicates whether they hold true in this case.

    Untitled Page 5#p_NxTGvCsM4sStrings can be compared in the same way.

    console.log("Aardvark" < "Zoroaster")
    // → true

    Untitled Page 5#p_No3uOP/bY2The way strings are ordered is roughly alphabetic but not really what you’d expect to see in a dictionary: uppercase letters are always “less” than lowercase ones, so "Z" < "a", and nonalphabetic characters (!, -, and so on) are also included in the ordering. When comparing strings, JavaScript goes over the characters from left to right, comparing the Unicode codes one by one.

    Untitled Page 5#p_fGKTuK5BBcOther similar operators are >= (greater than or equal to), <= (less than or equal to), == (equal to), and != (not equal to).

    console.log("Itchy" != "Scratchy")
    // → true
    console.log("Apple" == "Orange")
    // → false

    Untitled Page 5#p_tLooHn2QPjThere is only one value in JavaScript that is not equal to itself, and that is NaN (“not a number”).

    console.log(NaN == NaN)
    // → false

    Untitled Page 5#p_rcMZUIfGYRNaN is supposed to denote the result of a nonsensical computation, and as such, it isn’t equal to the result of any other nonsensical computations.

    Untitled Page 5#i_pdqDW7PeboLogical operators

    Untitled Page 5#p_nRCLrGwcCnThere are also some operations that can be applied to Boolean values themselves. JavaScript supports three logical operators: and, or, and not. These can be used to “reason” about Booleans.

    Untitled Page 5#p_h6pEyNS4IJThe && operator represents logical and. It is a binary operator, and its result is true only if both the values given to it are true.

    console.log(true && false)
    // → false
    console.log(true && true)
    // → true

    Untitled Page 5#p_T/V30CHY82The || operator denotes logical or. It produces true if either of the values given to it is true.

    console.log(false || true)
    // → true
    console.log(false || false)
    // → false

    Untitled Page 5#p_OxH3G7iBRzNot is written as an exclamation mark (!). It is a unary operator that flips the value given to it—!true produces false, and !false gives true.

    Untitled Page 5#p_qSXjNNI5/yWhen mixing these Boolean operators with arithmetic and other operators, it is not always obvious when parentheses are needed. In practice, you can usually get by with knowing that of the operators we have seen so far, || has the lowest precedence, then comes &&, then the comparison operators (>, ==, and so on), and then the rest. This order has been chosen such that, in typical expressions like the following one, as few parentheses as possible are necessary:

    1 + 1 == 2 && 10 * 10 > 50

    Untitled Page 5#p_EWJu4coIAhThe last logical operator I will discuss is not unary, not binary, but ternary, operating on three values. It is written with a question mark and a colon, like this:

    console.log(true ? 1 : 2);
    // → 1
    console.log(false ? 1 : 2);
    // → 2

    Untitled Page 5#p_xZmtGs+CeVThis one is called the conditional operator (or sometimes just the ternary operator since it is the only such operator in the language). The value on the left of the question mark “picks” which of the other two values will come out. When it is true, it chooses the middle value, and when it is false, it chooses the value on the right.

    Untitled Page 5#h_FewqJ8K2E+Empty values

    Untitled Page 5#p_Q/OIPtr8xYThere are two special values, written null and undefined, that are used to denote the absence of a meaningful value. They are themselves values, but they carry no information.

    Untitled Page 5#p_3veSnHeYusMany operations in the language that don’t produce a meaningful value (you’ll see some later) yield undefined simply because they have to yield some value.

    Untitled Page 5#p_43ZLcQuUDkThe difference in meaning between undefined and null is an accident of JavaScript’s design, and it doesn’t matter most of the time. In cases where you actually have to concern yourself with these values, I recommend treating them as mostly interchangeable.

    Untitled Page 5#h_AY+YGu6qyMAutomatic type conversion

    Untitled Page 5#p_I6CpHrk6+WIn the Introduction, I mentioned that JavaScript goes out of its way to accept almost any program you give it, even programs that do odd things. This is nicely demonstrated by the following expressions:

    console.log(8 * null)
    // → 0
    console.log("5" - 1)
    // → 4
    console.log("5" + 1)
    // → 51
    console.log("five" * 2)
    // → NaN
    console.log(false == 0)
    // → true

    Untitled Page 5#p_3GSZqcE16BWhen an operator is applied to the “wrong” type of value, JavaScript will quietly convert that value to the type it needs, using a set of rules that often aren’t what you want or expect. This is called type coercion. The null in the first expression becomes 0, and the "5" in the second expression becomes 5 (from string to number). Yet in the third expression, + tries string concatenation before numeric addition, so the 1 is converted to "1" (from number to string).

    Untitled Page 5#p_mw5To5JJ6QWhen something that doesn’t map to a number in an obvious way (such as "five" or undefined) is converted to a number, you get the value NaN. Further arithmetic operations on NaN keep producing NaN, so if you find yourself getting one of those in an unexpected place, look for accidental type conversions.

    Untitled Page 5#p_XbK88HE+DJWhen comparing values of the same type using ==, the outcome is easy to predict: you should get true when both values are the same, except in the case of NaN. But when the types differ, JavaScript uses a complicated and confusing set of rules to determine what to do. In most cases, it just tries to convert one of the values to the other value’s type. However, when null or undefined occurs on either side of the operator, it produces true only if both sides are one of null or undefined.

    console.log(null == undefined);
    // → true
    console.log(null == 0);
    // → false

    Untitled Page 5#p_hu+ZqjMro3That behavior is often useful. When you want to test whether a value has a real value instead of null or undefined, you can compare it to null with the == (or !=) operator.

    Untitled Page 5#p_N4OuWeYOwFBut what if you want to test whether something refers to the precise value false? Expressions like 0 == false and "" == false are also true because of automatic type conversion. When you do not want any type conversions to happen, there are two additional operators: === and !==. The first tests whether a value is precisely equal to the other, and the second tests whether it is not precisely equal. So "" === false is false as expected.

    Untitled Page 5#p_S/opLpHJcUI recommend using the three-character comparison operators defensively to prevent unexpected type conversions from tripping you up. But when you’re certain the types on both sides will be the same, there is no problem with using the shorter operators.

    Untitled Page 5#i_3jN0iK4yKWShort-circuiting of logical operators

    Untitled Page 5#p_CFbagJsQYKThe logical operators && and || handle values of different types in a peculiar way. They will convert the value on their left side to Boolean type in order to decide what to do, but depending on the operator and the result of that conversion, they will return either the original left-hand value or the right-hand value.

    Untitled Page 5#p_BFq+/JeBH9The || operator, for example, will return the value to its left when that can be converted to true and will return the value on its right otherwise. This has the expected effect when the values are Boolean and does something analogous for values of other types.

    console.log(null || "user")
    // → user
    console.log("Agnes" || "user")
    // → Agnes

    Untitled Page 5#p_+E3wg/b+tiWe can use this functionality as a way to fall back on a default value. If you have a value that might be empty, you can put || after it with a replacement value. If the initial value can be converted to false, you’ll get the replacement instead. The rules for converting strings and numbers to Boolean values state that 0, NaN, and the empty string ("") count as false, while all the other values count as true. So 0 || -1 produces -1, and "" || "!?" yields "!?".

    Untitled Page 5#p_LlkwKHpB6uThe && operator works similarly but the other way around. When the value to its left is something that converts to false, it returns that value, and otherwise it returns the value on its right.

    Untitled Page 5#p_IW4V8ztNjsAnother important property of these two operators is that the part to their right is evaluated only when necessary. In the case of true || X, no matter what X is—even if it’s a piece of program that does something terrible—the result will be true, and X is never evaluated. The same goes for false && X, which is false and will ignore X. This is called short-circuit evaluation.

    Untitled Page 5#p_WW6GFa4QbmThe conditional operator works in a similar way. Of the second and third values, only the one that is selected is evaluated.

    Untitled Page 5#h_ErccPg/l98Summary

    Untitled Page 5#p_K8XmHEfEpWWe looked at four types of JavaScript values in this chapter: numbers, strings, Booleans, and undefined values.

    Untitled Page 5#p_3rwX3Mq/e/Such values are created by typing in their name (true, null) or value (13, "abc"). You can combine and transform values with operators. We saw binary operators for arithmetic (+, -, *, /, and %), string concatenation (+), comparison (==, !=, ===, !==, <, >, <=, >=), and logic (&&, ||), as well as several unary operators (- to negate a number, ! to negate logically, and typeof to find a value’s type) and a ternary operator (?:) to pick one of two values based on a third value.

    Untitled Page 5#p_WHkzsJyNsJThis gives you enough information to use JavaScript as a pocket calculator but not much more. The next chapter will start tying these expressions together into basic programs.